A chromel-alumel thermocouple junction, which can be approximated with a sphere, has an effective diameter of 1 mm. It is used to measure the temperature of a gas flow with an effective heat-transfer coefficient of 500 W/m^2*C. (a) Determine the time constant of this thermocouple. (b) If the gas temperature suddenly increases by 100 C, how long will it take the thermocouple to attain a temperature rise within 1% of the gas temperature rise? (c) Find the answer to the previous questions if the diameter of the bead is doubled. (Assume that the heat-transfer coefficient remains the same)